# BUILDING FRACTIONS: Example 2

Rule 17:
To build a fraction is the reverse of reducing the fraction. Instead of searching for the 1 in a fraction so that you can reduce, you insert a 1 and build.

Example 3:
Create a fraction with 40 in the denominator that is equivalent to the fraction .
The answer is the fraction .

Solution:
This problem is a little more difficult because you can't multiply 50 by an integer to get 50. So we will first reduce the initial fraction. Reduce . .
is equivalent to . (You can verify this with your calculator.)
Recall that you can multiply any number by 1 without changing the value of the number. (Rule 6).
Multiply the fraction by 1.
Recall that 1 has many forms, look for the form of 1 that will result in a denominator of 40.

Since 5 8 = 40, use the fraction as 1.
Now can be written as . The product is .

We have created a fraction with a denominator equal to 40 that is equivalent to the fraction .

Check:
Now prove to yourself with your calculator that your answer is correct. Calculate 80 divided by 50 and calculate 64 divided by 40; both should yield the same answer. If you are correct, the answers are the same (equivalent) and you have successfully built a fraction.